Previous work has shown that massless tree amplitudes of the type I and IIA/B superstrings can be
simplified by expressing them as double copies between field-theory amplitudes and scalar
disk/sphere integrals, the latter containing all the alpha'-corrections. In this talk, I will introduce
similar double-copy constructions for the heterotic and bosonic string theories using an alpha'-
dependent field theory and the same disk/sphere integrals. Surprisingly, this field theory, built out of
dimension-six operators such as (DF)^2, has previously appeared in the double-copy construction
of conformal supergravity.